Polarisation

Overview

Polarisation is a property of transverse waves in which the oscillations are restricted to one direction or one plane perpendicular to the direction of propagation.

This topic helps distinguish transverse waves from longitudinal waves and explains optical devices such as sunglasses, LCD screens, and camera filters.

Definition

For a transverse wave, oscillations may occur in many directions perpendicular to wave travel. If these oscillations are confined to one direction only, the wave is polarised.

For light, plane polarisation means the electric field vector $\vec{E}$ oscillates in one plane.

Why It Matters

Polarisation is strong evidence that a wave is transverse. Since light can be polarised, light is transverse. Since sound in air is longitudinal, sound cannot be polarised.

Polarisation is also practically important in glare reduction, displays, photography, and stress analysis.

Key Representations

Why Only Transverse Waves Can Be Polarised

For transverse waves, oscillation is perpendicular to propagation. There are multiple possible vibration directions in the transverse plane, so polarisation is possible.

For longitudinal waves, oscillation is parallel to propagation. There is only one oscillation direction: forward-backward. Therefore longitudinal waves cannot be polarised.

Important consequence:

• sound in air is longitudinal, so sound cannot be polarised;
• light is transverse, so light can be polarised.

Plane Polarised Light

Natural light from common sources usually contains vibrations in many random transverse directions. This is unpolarised light.

If only one direction of electric-field vibration remains, the light is plane polarised or linearly polarised.

Polarisers

A polariser is a material or device that allows one direction of transverse vibration to pass while absorbing or blocking other directions.

For light, a polarising filter transmits only the component of the electric field vector $\vec{E}$ along its transmission axis. Unpolarised light entering a polariser becomes plane polarised, and intensity is reduced.

Transmission Axis and Analyser

Every polariser has a preferred direction called its transmission axis. Only the component parallel to this axis is transmitted effectively.

An analyser is a second polariser used to examine the state of polarisation of light. By rotating the analyser, transmitted intensity changes, confirming whether incoming light is polarised.

Two Polarisers

If two polarisers have parallel axes, transmitted light is maximum.

If their axes are at $90^{\circ }$, ideally no light is transmitted. This is why two crossed polarising sheets appear dark.

Malus’ Law

If plane polarised light enters an analyser at angle $\theta$ between its electric field direction and the analyser axis:

$$I=I_0{\cos }^2\theta$$

where $I_0$ is intensity before the analyser and $I$ is transmitted intensity.

Key cases:

$$\theta =0^{\circ }\Rightarrow I=I_0$$ $$\theta =90^{\circ }\Rightarrow I=0$$ $$\theta =45^{\circ }\Rightarrow I=\frac{1}{2}{I}_0$$

First Polariser for Unpolarised Light

Unpolarised light contains random vibration directions. On average, only half the intensity aligns with the polariser axis. After the first ideal polariser:

$$I=\frac{1}{2}{I}_{\text{incident}}$$

Demonstrations

A rope wave passing through a slit models polarisation. If the slit is parallel to the vibration direction, the wave passes. If the slit is perpendicular, it is blocked.

For light, rotating one polarising sheet behind another changes brightness continuously, with darkness at crossed position.

Applications

Polarised sunglasses reduce horizontally polarised glare reflected from roads or water. Photography filters control reflections and contrast. LCD screens use controlled polarisation states. Certain plastics rotate polarisation under stress and can be used for stress analysis.

Reflected light from non-metallic surfaces is often partially polarised, which is why polarised sunglasses reduce glare.

Common Mistakes

• Saying sound can be polarised.
• Saying all waves can be polarised.
• Treating an analyser as different physics from a polariser.
• Forgetting that only transverse waves can be polarised.

Links

• Main topic: Waves
• Related concept: Wave Basics
• Related concept: Intensity and Energy
• Related topic: Light Waves
• Related topic: Superposition of Waves